The answer is yes!!
House dust is a mixture of many substances including shed human skin, mold, animal hair and dander, fibers, and dust mite, dust mites body parts, and its excrement.
Dust mites are actually living creatures that are invisible to the naked eye. They are members of the arachnid family which includes their larger relatives the spider and the tick. Fortunately dust mites do not directly parasitize humans but they do feed off the dead skin particles shed by the human body. They also thrive in humid environments and love to snuggle in soft dust-collecting places including carpets, cloth covered furniture, stuffed animals and especially your bedding!!!!
The dust mite is not actually the direct cause of the human allergic response, its their body parts and fecal waste that mixes with household dust which ultimately becomes airborne creating potential for the allergic response.
In conclusion, It is possible to be allergic to house dust but not dust mites but most highly allergic individuals will be sensitive to both. Environmental control measures in the home and at work for both allergens is paramount for sustained and optimum allergy health.